This work outlines the main algorithms involved in a proposed bridge monitoring system based on ambient and earthquake vibration measurements. The monitoring system can be used to predict the existence, location and size of structural modifications in the bridge by monitoring the changes in the modal characteristics and updating the finite element model of the bridge based on the modal characteristics. Sophisticated system identification methods, combining information from a sensor network with the theoretical information built into a fi-nite element model for simulating structural behaviour, are incorporated into the monitoring system in order to track structural changes and identify the location, type and extent of these changes. Emphasis in this work is given on presenting theoretical and computational issues relating to structural modal identification and structural model updating methods. Specifical-ly, the proposed work outlines the algorithms and software that has been developed for com-puting the modal properties using ambient and earthquake data, as well as recent methodologies and software for finite element model updating using the modal characteristics. Various issues encountered in the optimization problems involved in model updating are demonstrated, including the existence of multiple local optima and the effects of weight values in conventional weighted modal residual methods for selecting the optimal finite element model. Selected features are demonstrated using vibration measurements from a four-span bridge of the Egnatia Odos motorway in Greece.